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You should always use as many digits as possible, so 1.008 g H for example, when doing calculations and save rounding for sig figs for when you have your final answer because if you round/use signings prematurely while you're still doing calculations it can affect your final answer. It wouldn't affect the final answer by too large of an extent. However, it could mean the difference between getting the question right or getting partial credit instead since it wouldn't be the exact answer the problem is looking for.
I prefer rounding to the third decimal place max when dealing with any element from the periodic table. That way, your answer is still very precise and you can also round to the nearest significant figure. Although it is tedious to use 1.008 during calculations, it often provides you with a well-calculated answer.
For me, I use Lavelle's IUPAC Periodic Table of the Elements that contains very specific constants. For example, Sodium (Na) has 22.98976928 g. Then, at the end, I round off depending on the smallest amount of significant figures.
Yeah, I personally try to use all of the digits given to me on the periodic table for an element/elements (specifically Lavelle's periodic table), and then I use as many steps as needed to solve the equation, without rounding whatsoever, until the very end, in which I will then round my answer as needed.
I tend to round to the nearest whole number when I'm trying to come up with like a guesstimate or if I'm doing like a multiple-choice test. For homework or free-response questions on tests, I tend to use the number on the periodic table of elements (so 1.008 for H and 15.99 for O). I round/do sig fig stuff at the very end.
I personally round it to the hundredth place of the decimal place and it usually gets me the same answer as the answer in the solutions manual so that should work but I guess the safest option would be using all the values in the periodic table.
I round to the hundredths place, but using Lavelle's IUPAC periodic table definitely helps with fixing inconsistencies when checking answers in the solution manual. I also think that because we all get the same periodic table during exams, we don't have to worry too much about these inconsistencies hurting us.
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